一类带有线性收获率的捕食者-食饵模型的稳定性分析  

Stability Analysis of a Predator-Prey Model with Linear Harvest Rate

作　　者：吴凡 焦玉娟[1] WU Fan;JIAO Yujuan(School of Mathematics and Computer Science,Northwest Minzu University,Lanzhou 730030,China)

机构地区：[1]西北民族大学数学与计算机科学学院

出　　处：《湖北民族学院学报（自然科学版）》2019年第3期282-286,共5页Journal of Hubei Minzu University(Natural Science Edition)

基　　金：中央高校重大培育项目(31920190057)

摘　　要：基于一类带有Holling-II型功能反应函数的捕食-食饵模型,考虑了捕食者和食饵的线性收获率.并对该模型进行了一系列的理论分析,首先考虑了模型满足生物学意义解的存在性和有界性,其次求出了模型的平衡点,判断出平衡点稳定的条件以及分析了稳定性变化产生的Hopf分支.最后,通过计算机模拟来验证理论推导,结合实际的生物意义对模型进行说明.In this paper,we consider the linear harvest rate of predators and prey based on a predator-prey model with Holling-II functional response function,and carried out a series of theoretical analysis on the model.First,we consider whether the model has the existence and boundedness of biologically meaningful solutions,and then find the equilibrium point of the system,and calculate whether the equilibrium point is stable and what conditions should be met if it is stable.Finally,we calculate the curve of the numerical simulation solution and explain the system in a accordance with the actual biological significance.

关 键 词：捕食者-食饵模型 动力系统 平衡点 数值模拟 

分 类 号：Q141[生物学—生态学]